Bias in Estimating Multivariate and Univariate Diffusions

Multivariate continuous time models are now widely used in economics and finance. Empirical applications typically rely on some process of discretization so that the system may be estimated with discrete data. This paper introduces a framework for discretizing linear multivariate continuous time sys...

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Main Authors: WANG, Xiaohu, PHILLIPS, Peter C. B., YU, Jun
Format: text
Language:English
Published: Institutional Knowledge at Singapore Management University 2010
Subjects:
OLS
Online Access:https://ink.library.smu.edu.sg/soe_research/1235
https://ink.library.smu.edu.sg/context/soe_research/article/2234/viewcontent/multidiffusion13.pdf
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spelling sg-smu-ink.soe_research-22342019-04-21T01:15:43Z Bias in Estimating Multivariate and Univariate Diffusions WANG, Xiaohu PHILLIPS, Peter C. B. YU, Jun Multivariate continuous time models are now widely used in economics and finance. Empirical applications typically rely on some process of discretization so that the system may be estimated with discrete data. This paper introduces a framework for discretizing linear multivariate continuous time systems that includes the commonly used Euler and trapezoidal approximations as special cases and leads to a general class of estimators for the mean reversion matrix. Asymptotic distributions and bias formulae are obtained for estimates of the mean reversion parameter. Explicit expressions are given for the discretization bias and its relationship to estimation bias in both multivariate and in univariate settings. In the univariate context, we compare the performance of the two approximation methods relative to exact maximum likelihood (ML) in terms of bias and variance for the Vasicek process. The bias and the variance of the Euler method are found to be smaller than the trapezoidal method, which are in turn smaller than those of exact ML. Simulations suggest that for plausible parameter settings the approximation methods work better than ML, the bias formulae are accurate, and for scalar models the estimates obtained from the two approximate methods have smaller bias and variance than exact ML. For the square root process, the Euler method outperforms the Nowman method in terms of both bias and variance. Simulation evidence indicates that the Euler method has smaller bias and variance than exact ML, Nowman’s method and the Milstein method. 2010-10-01T07:00:00Z text application/pdf https://ink.library.smu.edu.sg/soe_research/1235 https://ink.library.smu.edu.sg/context/soe_research/article/2234/viewcontent/multidiffusion13.pdf http://creativecommons.org/licenses/by-nc-nd/4.0/ Research Collection School Of Economics eng Institutional Knowledge at Singapore Management University OLS Continuous Time Bias Reduction Di¤usion Euler approximation Mil-stein approximation Multivariate Vasicek model. Econometrics
institution Singapore Management University
building SMU Libraries
continent Asia
country Singapore
Singapore
content_provider SMU Libraries
collection InK@SMU
language English
topic OLS
Continuous Time
Bias Reduction
Di¤usion
Euler approximation
Mil-stein approximation
Multivariate
Vasicek model.
Econometrics
spellingShingle OLS
Continuous Time
Bias Reduction
Di¤usion
Euler approximation
Mil-stein approximation
Multivariate
Vasicek model.
Econometrics
WANG, Xiaohu
PHILLIPS, Peter C. B.
YU, Jun
Bias in Estimating Multivariate and Univariate Diffusions
description Multivariate continuous time models are now widely used in economics and finance. Empirical applications typically rely on some process of discretization so that the system may be estimated with discrete data. This paper introduces a framework for discretizing linear multivariate continuous time systems that includes the commonly used Euler and trapezoidal approximations as special cases and leads to a general class of estimators for the mean reversion matrix. Asymptotic distributions and bias formulae are obtained for estimates of the mean reversion parameter. Explicit expressions are given for the discretization bias and its relationship to estimation bias in both multivariate and in univariate settings. In the univariate context, we compare the performance of the two approximation methods relative to exact maximum likelihood (ML) in terms of bias and variance for the Vasicek process. The bias and the variance of the Euler method are found to be smaller than the trapezoidal method, which are in turn smaller than those of exact ML. Simulations suggest that for plausible parameter settings the approximation methods work better than ML, the bias formulae are accurate, and for scalar models the estimates obtained from the two approximate methods have smaller bias and variance than exact ML. For the square root process, the Euler method outperforms the Nowman method in terms of both bias and variance. Simulation evidence indicates that the Euler method has smaller bias and variance than exact ML, Nowman’s method and the Milstein method.
format text
author WANG, Xiaohu
PHILLIPS, Peter C. B.
YU, Jun
author_facet WANG, Xiaohu
PHILLIPS, Peter C. B.
YU, Jun
author_sort WANG, Xiaohu
title Bias in Estimating Multivariate and Univariate Diffusions
title_short Bias in Estimating Multivariate and Univariate Diffusions
title_full Bias in Estimating Multivariate and Univariate Diffusions
title_fullStr Bias in Estimating Multivariate and Univariate Diffusions
title_full_unstemmed Bias in Estimating Multivariate and Univariate Diffusions
title_sort bias in estimating multivariate and univariate diffusions
publisher Institutional Knowledge at Singapore Management University
publishDate 2010
url https://ink.library.smu.edu.sg/soe_research/1235
https://ink.library.smu.edu.sg/context/soe_research/article/2234/viewcontent/multidiffusion13.pdf
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